Superposition coding will be discussed in multi-user communications systems. Multi-user communication systems involve several transmitters and receivers communicating with each other and may use one or more communications methods. In general, multi-user communication methods may be categorized into one of two scenarios:                (a) A single transmitter communicating with several receivers, commonly referred to as a broadcast communications method, and        (b) Several transmitters communicating to a common receiver, which is commonly referred to as a multiple-access communications method.        
The broadcast communications method is commonly known in the communications and information theory literature as the ‘broadcast channel’ and will be referred to as such in the rest of this document. The ‘broadcast channel’ refers to the physical communication channels between the transmitter and the multiple receivers as well as the communication resources used by the transmitter to communicate. Similarly, the multiple-access communications method is widely known as the ‘multiple-access channel’ and the remainder of this document will use this terminology. Once again, the ‘multiple-access channel’ refers to the physical communication channels between the multiple transmitters and the common receiver, along with the communication resources used by the transmitters. The broadcast communications method is frequently used to implement the downlink communication channel in a typical cellular wireless system, where the base station broadcasts to a plurality of wireless terminals, while the uplink channel in such a system is commonly implemented using the multiple-access communications method, where a plurality of wireless terminals may transmit signaling to a base station.
The transmission resource in the multi-user communication system can generally be represented in time, frequency or code space. Information theory suggests that the capacity of the system can be increased in both scenarios, in particular, by transmitting to multiple receivers simultaneously in the case of the broadcast communications method, or by allowing multiple transmitters to transmit simultaneously in the case of the multiple-access communications method, over the same transmission resource, e.g., over the same frequencies at the same time. In the case of the broadcast communications method, the technique used to transmit simultaneously to multiple users over the same transmission resource is also known as ‘superposition coding’. In the context of the present invention, controlled superposition coding is shown to be a valuable practical technique in both broadcast and multiple-access communications methods.
The advantages of superposition coding will be apparent in view of the following discussion of transmission techniques for the broadcast communications method. Consider a single transmitter communicating with two receivers, whose channels can be described by ambient Gaussian noise levels of N1 and N2, with N1<N2, i.e., the first receiver operates over a stronger channel than the second receiver. Assume that the communication resources available to the transmitter are a total bandwidth of W, and a total power of P. The transmitter may employ several strategies to communicate with the receivers. FIG. 1 includes a graph 100 which plots achievable rates in a broadcast channel, for a first user, with a stronger receiver and a second receiver, with a weaker receiver, under three different transmission strategies. The vertical axis 102 of FIG. 1 represents the rate for the stronger receiver, while the horizontal axis 104 represents the rate for the weaker receiver.
First, consider the strategy where the transmitter multiplexes between the two receivers in time, allocating all its resources to one receiver at a time. If the fraction of time spent communicating with the first (stronger) receiver is denoted by α, it is easy to show that the achievable rates for the two users satisfy
                                          R            1                    ≤                      α            ⁢                                                  ⁢            W            ⁢                                                  ⁢                          log              ⁡                              (                                  1                  +                                      P                                          N                      1                                                                      )                                                    ,                                          R          2                ≤                              (                          1              -              α                        )                    ⁢          W          ⁢                                          ⁢                      log            ⁡                          (                              1                +                                  P                                      N                    2                                                              )                                          
As the fraction of time spent serving the first user, α, varies, the rates achieved by the above equations are represented with the straight line 106 in FIG. 1 representing the Time Division Multiplexing (TDM) strategy. Now consider a different transmission strategy where the transmitter allocates a certain fraction of the bandwidth, β, and a fraction of the available power, γ, to the first user. The second user gets the remaining fractions of bandwidth and power. Having allocated these fractions, the transmitter communicates with the two receivers simultaneously. Under this transmission strategy, the rate region can be characterized by the following equations
                                          R            1                    ≤                      β            ⁢                                                  ⁢            W            ⁢                                                  ⁢                          log              ⁡                              (                                  1                  +                                                            α                      ⁢                                                                                          ⁢                      P                                                              N                      1                                                                      )                                                    ,                                          R          2                ≤                              (                          1              -              β                        )                    ⁢          W          ⁢                                          ⁢                                    log              ⁡                              (                                  1                  +                                                                                    (                                                  1                          -                          α                                                )                                            ⁢                      P                                                              N                      2                                                                      )                                      .                              
The rates achieved by the above equations are visualized intuitively from the convex curve segmented line 108 in FIG. 1 representing the frequency division multiplexing (FDM) strategy. It is evident that the strategy of dividing the available power and bandwidth between the two users in an appropriate manner outperforms the time-division partition of resources. However, the second strategy is not yet the optimal one.
The supremum of the rate regions achievable under all transmission strategies is the broadcast capacity region. For the Gaussian case, this region is characterized by the equations
                                          R            1                    ≤                      W            ⁢                                                  ⁢                          log              ⁡                              (                                  1                  +                                                            α                      ⁢                                                                                          ⁢                      P                                                              N                      1                                                                      )                                                    ,                                                      R            2                    ≤                      W            ⁢                                                  ⁢                          log              ⁡                              (                                  1                  +                                                                                    (                                                  1                          -                          α                                                )                                            ⁢                      P                                                                                      α                        ⁢                                                                                                  ⁢                        P                                            +                                              N                        2                                                                                            )                                                    ,            and is indicated by the dashed curve line 110 in FIG. 1 representing capacity. It was shown by Thomas Cover in T. M. Cover, Broadcast Channels, IEEE Transactions on Information Theory, IT-18 (1):2 14, 1972, that a communication technique called superposition coding could achieve this capacity region. In this technique, the signals to different users are transmitted with different powers in the same transmission resource and superposed on each other. The gains achievable through superposition coding surpass any other communication technique that requires splitting of the transmission resource among different users.
The basic concept of superposition coding is illustrated in graph 200 of FIG. 2. Graph 200 includes a vertical axis 202 representing quadrature and a horizontal axis 204 representing in-phase. While this example assumes QPSK modulation, the choice of modulation sets is not restrictive in general. Also, this example is sketched out for two users with the concept generalizing in a straightforward manner to multiple users. Assume that the transmitter has a total transmit power budget P. Suppose that the first receiver, referred to as ‘weaker receiver’, sees larger channel noise and the second receiver, referred to as ‘stronger receiver’, sees smaller channel noise. Four circles filled in with a pattern 205 represent the QPSK constellation points to be transmitted at high power (better protected), (1−α)P, to the weaker receiver, where arrow 206 provides a measure of the high power QPSK transmission strength. Meanwhile, additional information is conveyed to the stronger receiver at low power (less protected), αP, also using a QPSK constellation, where arrow 207 provides a measure of the lower power QPSK transmission strength. The actually transmitted symbols, which combine both the high power and low power signals, are represented as the blank circles 208 in FIG. 2. A key concept that this illustration conveys is that the transmitter communicates to both users simultaneously using the same transmission resource. In this document, the high power signal is also called a protected signal, and the low power signal is also a called regular signal.
The receiver strategy is quite straightforward. The weaker receiver sees the high power QPSK constellation with a low-power signal superposed on it. The Signal-to-Noise Ratio (SNR) experienced by the weaker receiver may be insufficient to resolve the low-power signal, so the low power signal appears as noise and slightly degrades the SNR when the weaker receiver decodes the high power signal. On the other hand, the SNR experienced by the stronger receiver is sufficient to resolve both the high power and low power QPSK constellation points. The stronger receiver's strategy is to decode the high-power points (which are intended for the weaker receiver) first, remove their contribution from the composite signal, and then decode the low-power signal.
However, in practice, this strategy normally does not work well. Any imperfections in cancellation of the high-power signal manifest themselves as noise to the decoder recovering the low-power signal.
In light of the above discussion, it is clear that a need exists for novel methods and apparatus that will allow communications systems to operate in a broadcast and/or multiple access communications method using controlled superposition coding to take advantage of the benefits of higher achievable rates in the channel, yet overcome the practical difficulties encountered of imperfect cancellation of the high power signal and the complexity and cost associated with joint decoder approach.